The MATHEMATICA® software system is a powerful computational tool that can evaluate general symbolic expressions, as well as mathematical and numeric expressions. A unifying feature of MATHEMATICA® is that everything is internally represented as a symbolic expression, with all more specific data types treated as special cases—symbols to which additional rules apply. MATHEMATICA® is an interpreted language, with a notion of “evaluation” of symbolic expressions. Evaluation involves applying to any symbolic expression all transformation rules that fit that expression.
In the MATHEMATICA® software system, a user can create interactive electronic documents referred to as “notebooks.” Various expressions, including numeric and symbolic expressions, can be entered into a notebook via a keyboard, for example, and a user can cause the expression to be evaluated.
Various expressions, including numeric and symbolic expressions, can be entered into a notebook via a keyboard, for example, and a user can cause the expression to be evaluated. Some expressions may be used to create graphical displays in a notebook. One example is a built-in function Plot. A user could type into the notebook the expression “Plot[y^2, {y, 0, 5}]”, and the MATHEMATICA® software system evaluates the expression “Plot[y^2, {y, 0, 5}]” to generate a plot of the function y2 versus the variable y between y=0 to y=5. The generated plot is then displayed in the notebook. The MATHEMATICA®software system provides other built-in functions for creating graphical displays such as ContourPlot, DensityPlot, Plot3D, ParametricPlot, ParametricPlot3D, etc. Further, built-in functions are provided for displaying tables and matrices.
Spreadsheet software applications, such as the EXCEL® software application available from Microsoft Corporation, permit a user to create spreadsheets comprising grids of cells. In a spreadsheet, a value in one cell may be dependent upon a value in one or more other cells. For example, a user may assign a formula to a first cell that uses a value from a second cell. Then, the spreadsheet application will calculate an output of the formula using the value from the second cell, and will display the calculated value in the first cell. When a user changes the value of the first cell, the spreadsheet application will recalculate the value of the formula of the second cell. Such applications require inputs to the first cell in a numeric form, need an explicit formula taking numeric input to relate the contents of the second cell to the numeric values in the first, and output numeric output to the second cell.